A gardner plants tomatoes in a square pattern. She surrounds them with marigolds. x = number of tomatoes...?

Question

x = number of tomato plants
y = number of marigolds

The diagrams that were given on the sheet show the patterns of tomato plants and marigolds:

Diagram 1: One tomato surrounded by 7 marigolds:
(M = marigold)
(T = Tomato)
1 Tomato
8 Marigolds
MMM
MTM
MMM

Diagram 2:
4 Tomatoes
16 Marigolds
MMMMM
MT TM
M M
MT TM
MMMMM

Diagram 3:
9 Tomatoes
25 Marigolds
MMMMMMM
MT T TM
M M
MT T TM
M M
MT T TM
MMMMMMM

Alright, that's really weird, isn't it? Somehow I'm supposed to use radicals to answer the following questions:

a. If there were 16 tomato plants, how many marigolds would be needed?
b. If there were 48 tomato plants, how many marigolds would be needed?
c. Write in equation INVOLVING ROOTS that relates the number of tomato plants (x) to the number of marigolds (y)
d. For what values of x and y would the number of tomato plants = the number of marigolds?

PLEASE help me on this! I have NO CLUE what I'm doing! Thanks in advance!!!!!

Answer 1

I think you have a mistake in diagram 3: Your picture shows only 24 marigolds, but your text says 25. I like 24!

c. y = 8√T
a. y = 8*4 = 32
b. y = 8*4*√3 = 55.42 (48 tomatoes cannot be arranged in a square!) If the # is really 49, then y = 8*7 = 56
d. x = y = 0

Answer 2

Okay, I don't know the answer to this for sure, but I'll take a guess.

In scenario #1, you have 1 tomato + 8 marigolds. Since there is only 1 marigold, all you need to do is surround it.

In scenario #2, you have 4 tomatoes / 16 Marigolds.

In scenario #3, you have 9 tomatoes / 25 Marigolds.


Scenarios #2 / #3 in my mind present perfect squares. That is, 4 = 2^2 (Two to the power of 2) or (2 squared). 16 is 4 squared.

In no three, you have the same thing: 9 = 3^2, 25 = 5^2. The difference between them is two.

That is to say, I took the square of 2 and the square of 4.

Then I took the square of 3, and the square of 5.

SOOOO...

If there were 16 tomato plants, which is 4^2, I think I would add two, and square it. This gives me 36 marigolds.

If there were 48 plants, I cannot get a perfect square. So, I'll break this down into perfect squares. 48 = 6^2 + 3^2 + 3
Then, I'll add two to my perfect squares.

(6+2)^2 + (3+2)^2 = 64+25 =89, and then I need either 8 marigolds for each of the three remaining tomatoes (24) or maybe I just need to surround the last three:

MMMMM
MTTT M
MMMMM

In which case, that would be 12 more. So...you make the caall.

The equation I would write would be:

sqrt x = sqrt y - 2

And then for what values of x & y would the numbers be the same?

I wish I could help you on that last one.

Good luck!

Mysstere

Answer 3

how you'll boost tomatoes is organically, yet when you're literally not into that type of issue, you are able to regulate your backyard round to living house for organic and organic turning out to be. i'm an organic and organic gardener and that i have stumbled on that the perfect issue to fertilize tomatoes with is a reliable compost tea and hydrolyzed fish. I usually attempt this about 2 weeks when I plant them and each and each month after that because they are nonetheless turning out to be (plus it truly is difficult to burn out your flora on reliable organic and organic fertilizer so dont trouble about putting a touch too a lot). Its also a reliable theory to address the soil with this a week before planting to placed each and each of the valuable microorganisms into the soil to practice it for flora. wish this enables.